Id trapezium ABCD (adjoining figure), side AB || side DC, diagonals AC

1.	Id trapezium ABCD (adjoining figure), side AB \|\| side DC, diagonals AC and BD intersect in point O. If AB = 20, DC = 6, OB = 15, then find OD.
Answer» side AB \|\| side DC [Given] and seg BD is their transversal. ∴ ∠DBA ≅ ∠BDC [Alternate angles] ∴ ∠OBA ≅ ∠ODC (i) [D – O – B] In ∆OBA and ∆ODC ∠OBA ≅ ∠ODC [From (i)] ∠BOA ≅ ∠DOC [Vertically opposite angles] ∴ ∆OBA ~ ∆ODC [AA test of similarity] ∴ OB/OD = AB/DC = [Corresponding sides of similar triangles] ∴ 15/OD = 20/6 ∴ OD = x = (15 x 6)/20 ∴ OD = 4.5 units

Id trapezium ABCD (adjoining figure), side AB || side DC, diagonals AC and BD intersect in point O. If AB = 20, DC = 6, OB = 15, then find OD.

Answer»

side AB || side DC [Given]

and seg BD is their transversal.

∴ ∠DBA ≅ ∠BDC [Alternate angles]

∴ ∠OBA ≅ ∠ODC (i) [D – O – B]

In ∆OBA and ∆ODC

∠OBA ≅ ∠ODC [From (i)]

∠BOA ≅ ∠DOC [Vertically opposite angles]

∴ ∆OBA ~ ∆ODC [AA test of similarity]

∴ OB/OD = AB/DC = [Corresponding sides of similar triangles]

∴ 15/OD = 20/6

∴ OD = x = (15 x 6)/20

∴ OD = 4.5 units

Discussion

No Comment Found

Related InterviewSolutions

Given below are some triangles and lengths of line segments. Identify in which figures, ray PM is the bisector of `/_QPR`.
In the figure, `PS=3`, `SQ=6`, `QR=5`, `PT=x` and `TR=y`. Give any two pairs of values of `x` and `y` such that line `ST||` side `QR`.
As shown in the adjoining figure, two poles of height 8 m and 4 m are perpendicular to the ground. If the length of shadow of smaller pole due to sunlight is 6 m, then how long will be the shadow of the bigger pole at the same time?
`DeltaLMN~DeltaPQR`, `9xxA(DeltaPQR)=16xxA(DeltaLMN)`. If `QR=20`, then find `MN`.
As shown in the figures, two poles of height 8m and 4m are perpendicular to the groudn. If the length of shadow smaller pole due to sunlight is 6 m then long will be the shadow of the bigger pole of the same time?
In the adjoining figure, `BP bot AC`, `CQ bot AB`, `A-P-C`, `A-Q-B`. Complete the following activity to Prove `DeltaAPB~DeltaAQC`. In `DeltaAPB` and `DeltaAQC` `/_APB=square^(@)`…….`(1)` `/_AQC=square^(@)`……..`(2)` `:./_APB~=/_AQC`…....(`square`) `:.DeltaAPB~DeltaAQC`......(`square`)
In `DeltaMNP, NQ` is a bisector of `/_N`. If `MN=5, PN=7, MQ=2.5,` the find QP.
In the figure seg `PQ||` seg DE, `A(DeltaPQF)=20` units `PF=2DP`,then find `A(square DPQE)` by completing the following activity: Activity: `A(DeltaPQF)=20` sq units, `PF=2DP`. Let us assume `DP=x` `:.PF=2x` `DF=DE+square=square+square=3x` In `DeltaFDE` and `DeltaFPQ`. `/_FDE~=/_square` ..........(Corresponding angles) `/_FED~=/_square` .....(Corresponding angles) `:.DeltaFDE~DeltaFPQ` .....(AA test) `:.(A(DeltaFDE))/(A(DeltaFPQ))=(square)/(square)=((3x)^(2))/((2x)^(2))=9/4` `A(DeltaFDE)=9/4A(DeltaFPQ)=9/4xxsquare=square` `A(squareDPQE)=A(DeltaFDE)-A(DeltaFPQ)` `=square-square` `=square`
In figure `XY||` seg AC. If `2AX=3BX` and `XY=9`, complete the activity to find the value of AC. Activity: `2AX=3BX` `:.(AX)/(BX)=(square)/(square)` `:.(AX+BX)/(BX)=(square+square)/(square)`.........(By componendo) `:.(AB)/(BX)=(square)/(square)`.............1`DeltaBCA~DeltaBYX`.......(`square` test of similarity) `:.(BA)/(BX)=(AC)/(XY)` ..............(Corresponding sides of similar triangles) `:.(square)/(square)=(AC)/9` `:.AC=square` ...........[From 1]
In the adjoining figure, seg `XY||` seg `AC`, IF `3AX=2BX` and `XY=9` then find the length of `AC`.

Id trapezium ABCD (adjoining figure), side AB || side DC, diagonals AC and BD intersect in point O. If AB = 20, DC = 6, OB = 15, then find OD.

Discussion

No Comment Found

Related InterviewSolutions

Reply to Comment